The broad, long-term objective and specific aims is to establish the utility of using unrelated matched and partially mismatched cord blood cells as a source of hematopoietic stem cells for allogeneic grafting in adult patients with malignant diseases. Cord blood has been used successfully to reconstitute pediatric patients following myeloablative preparatory regimens. However, the utility of these cells in the adult populations remains limited. If the success encountered in the pediatric population could be expanded to adults, then the current difficulties with finding acceptable histocompatible donors could be overcome in the majority of patients. This application proposes to overcome many of the limitations of cord blood transplantation in the adult population through the use of a non-myeloablative regimen. This research project will: 1.) Conduct a clinical trial utilizing a non-myeloablative preparatory regimen followed by infusion of a single unit of cord blood cells, 2.) Conduct a clinical trial utilizing a non-myeloablative preparatory regimen followed by infusion of multiple units of cord blood cells and 3.) Perform a detailed measurement of immune recovery following non-myeloablative CBT compared to conventional CBT in adult patients. The preliminary results suggests that engraftment can occur in adult patients treated for malignant diseases and that while the numbers of patients treated are small, the overall outcome clinically and based on laboratory parameters are encouraging. The results will provide an indication of the percentage of time where engraftment does or does not occur and how it is related to other clinical factors such as the degree of mismatching at the major histocompatibility complex. Moreover, the overall incidence of graft-versus-host disease and the possible graft-versus-leukemia effect will also be analyzed. More importantly, the manner in which the immune system recovers following the establishment of hematopoiesis will be delineated and correlation with clinical outcome will also be investigated. It is expected that at the end of these studies, the utility of cord blood following non-myeloablative regimens will be well defined and a follow up prospective randomized study will be planned comparing the approach outlined in this application with the best alternative approach at that timepoint.